Question

3) (1 - 3x)(x + 2)(3 - x) < 0;4) x(5 - x)(6 - x) < 0.​

Answer 1

Ответ:

вот ответ не благодори :):)))

Answer 2

Ответ:

3) (-∞; -2) ∪ (3; + ∞); 4) (-∞; 0) ∪ (6; + ∞)

Объяснение:

3) (1 - 3x)(x + 2)(3 - x) < 0;

1 - 3x < 0  або  x + 2 < 0  або  3 - x < 0  

- 3x < - 1            x  < - 2              - x < - 3

 x > 1/3                                         x > 3    

х (-∞; -2) ∪ (3; + ∞)

4) x(5 - x)(6 - x) < 0.

x < 0. або 5 - x < 0 або 6 - x < 0.​

x < 0.           - x < -5         - x < -6.​

                     x > 5              x > 6

х (-∞; 0) ∪ (6; + ∞)

Answer 3

To solve these inequalities, we need to find the intervals where the expressions are less than zero (negative). We can achieve this by analyzing the sign changes of each factor and then determining the intervals in which the product is negative.

Let's solve each inequality step by step:

1) (1 - 3x)(x + 2)(3 - x) < 0

First, let's find the critical points by setting each factor equal to zero:

1 - 3x = 0 => x = 1/3 x + 2 = 0 => x = -2 3 - x = 0 => x = 3

Now, let's create a sign chart for the intervals separated by these critical points:

Interval 1: x < -2 Interval 2: -2 < x < 1/3 Interval 3: 1/3 < x < 3 Interval 4: x > 3

For each interval, let's pick a test point and evaluate the expression (1 - 3x)(x + 2)(3 - x) to determine its sign:

Interval 1 (e.g., x = -3): (-)(-)(+) = - Interval 2 (e.g., x = 0): (+)(-)(+) = + Interval 3 (e.g., x = 2): (+)(+)(-) = - Interval 4 (e.g., x = 4): (+)(+)(+) = +

From the sign chart, we can see that the expression is negative in Interval 1 and Interval 3. Therefore, the solution to the inequality is:

-2 < x < 1/3 or 3 < x

2) x(5 - x)(6 - x) < 0

Again, let's find the critical points by setting each factor equal to zero:

x = 0 5 - x = 0 => x = 5 6 - x = 0 => x = 6

Create a sign chart for the intervals:

Interval 1: x < 0 Interval 2: 0 < x < 5 Interval 3: 5 < x < 6 Interval 4: x > 6

Evaluate the expression x(5 - x)(6 - x) for each interval using test points:

Interval 1 (e.g., x = -1): (-)(-)(-) = - Interval 2 (e.g., x = 2): (+)(+)(-) = - Interval 3 (e.g., x = 5.5): (+)(-)(-) = + Interval 4 (e.g., x = 7): (+)(+)(+) = +

From the sign chart, we can see that the expression is negative in Interval 1 and Interval 2. Therefore, the solution to the inequality is:

0 < x < 5

In summary:

1. Solution: -2 < x < 1/3 or 3 < x
2. Solution: 0 < x < 5